Can an absolute value ever be negative? So can this equation have any valid solution?

alle1985 wrote:but what can i do for |x^2-3x|=2?

The general process for solving absolute-value equations may be found here. For this particular equation, locate the zeroes of x^2 - 3x (being x = 0 and x = 3), and determine the intervals of positivity and negativity (which may easily be discerned from the graph of y = x^2 - 3x). Then solve the derivative equations x^2 - 3x = 2 and -x^2 + 3x = 2 on the relevant intervals.

Remember to verify any solutions against the conditions. For instance, is the solution value within the relevant interval?